> On 15 Dec 2012, Robert hansen wrote:> > > One of his observations was that students will> accept> > that 0.333... is 1/3 but have trouble accepting> that> > 0.999... is 1.> > I wonder if "accepting" this would be a problem if> these students had been taught how to convert a> repeating decimal into a fraction, as we were when I> was in high school?> > Let x=0.999...> then 10x=9.999...> then 9x=9> and x=1

When I taught Algebra I, I would show students the method you cited. Many students reacted as if it were a trick - like when one 'proves' that 2 = 1 by using an illegal divide-by-zero step.